A trace finite element method for a class of coupled bulk-interface transport problems

In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling of transport and diffusion of surfactants in two-phase flows. The model considered here accounts for adsorption-desorption of the surfactants at a sharp interface between two fluids and their transport and diffusion in both fluid phases and along the interface. The paper gives a well-posedness analysis for the system of bulk-surface equations and introduces a finite element method for its numerical solution. The finite element method is unfitted, i.e., the mesh is not aligned to the interface. The method is based on taking traces of a standard finite element space both on the bulk domains and the embedded surface. The numerical approach allows an implicit definition of the surface as the zero level of a level-set function. Optimal order error estimates are proved for the finite element method both in the bulk-surface energy norm and the $L^2$-norm. The analysis is not restricted to linear finite elements and a piecewise planar reconstruction of the surface, but also covers the discretization with higher order elements and a higher order surface reconstruction

Germany's fragile leadership role in European air defence: the need for adjustments at all levels of the European Sky Shield Initiative

With the European Sky Shield Initiative (ESSI), Germany has made its claim as the leader in European air defence. Taking a joint approach to defence is a good step for­ward, but difficult to implement. Important European partners, above all France and Italy, are currently unwilling to follow Germany’s lead. The lack of political unity shows that Germany’s proposal does not take European security interests sufficiently into account, has failed to convince partners, and leaves many questions unanswered on the strategic, military, industrial, and economic levels. If the ESSI is to noticeably improve Europe’s air defence protection, Berlin must provide answers about strategic balance, the development of the European defence industry, and militarily effective solutions. The acquisition of individual military capabilities will not produce a Euro­pean Sky Shield. (Autorenreferat

Aktuelle Themen in der Unternehmensbewertung

Die vorliegende kumulative Dissertationsschrift beschäftigt sich mit finanzwissenschaftlichen Fragestellungen im Bereich der Unternehmensbewertung. Dabei wurden aktuelle Themen diskutiert, die in Theorie oder Praxis ungelöste Probleme darstellen. Hervorzuheben ist an dieser Stelle, dass sich die ersten drei Artikel mit dem Werteinfluss der Zinsschanke auf den Wert von fremdfinanzierungsbedingten Steuerersparnissen (Tax Shield) beschäftigen. Die drei darauf folgenden Artikel beschäftigen sich schwerpunktmäßig mit der konsistenten Modellierung von Finanzierungspolitiken und dem Werteinfluss der Insolvenzmöglichkeit von Unternehmen. Der siebte und achte Artikel haben die Kapitalstruktur und weitere wichtige Parameter für die Unternehmensbewertung zum Thema.:1. Thematische Einordnung und Forschungsbeitrag … 1 2. Die Bewertung der Zinsschranke … 14 3. Zinsschranke, Unternehmensbewertung und APV-Ansatz - eine Anmerkung zum Beitrag von Förster/Stöckl/Brenken (ZfB 2009, S. 985 ff.) … 59 4. Der Einfluss der Zinsschranke auf den Unternehmenswert … 84 5. Tax Shield, Insolvenz und Zinsschranke … 109 6. Tax Shield, Insolvenzwahrscheinlichkeit und Zinsschranke - eine empirische Analyse … 169 7. The Impact of Credit Rating and Frequent Refinancing on Firm Value … 211 8. Zur Überprüfung von Kapitalstrukturtheorien in einer von Krisen geprägten Zeit … 258 9. Die Kapitalmarktdaten von www.finexpert.info und der Fachverlag Gruppe … 30

A Trace Finite Element Method for Vector-Laplacians on Surfaces

We consider a vector-Laplace problem posed on a 2D surface embedded in a 3D domain, which results from the modeling of surface fluids based on exterior Cartesian differential operators. The main topic of this paper is the development and analysis of a finite element method for the discretization of this surface partial differential equation. We apply the trace finite element technique, in which finite element spaces on a background shape-regular tetrahedral mesh that is surface-independent are used for discretization. In order to satisfy the constraint that the solution vector field is tangential to the surface we introduce a Lagrange multiplier. We show well-posedness of the resulting saddle point formulation. A discrete variant of this formulation is introduced which contains suitable stabilization terms and is based on trace finite element spaces. For this method we derive optimal discretization error bounds. Furthermore algebraic properties of the resulting discrete saddle point problem are studied. In particular an optimal Schur complement preconditioner is proposed. Results of a numerical experiment are included

The influence of environmental parameters on the thermographic analysis of the building envelope

Typically, thermographic measurements are used to analyze the building envelope in a qualitative way (e.g. detection of thermal bridges, missing insulation, etc.). Besides, thermography can also be used to obtain surface temperatures, which can give an indication of the thermal performance of the building envelope. In this paper the influence of the most important environmental parameters on the thermographic analysis of different wall types is examined using a multivariable parameter study. This results in guidelines that are in good accordance with the existing guidelines. Furthermore some remarks were made concerning the ambiguities in the existing guidelines

Driving Context into Text-to-Text Privatization

\textit{Metric Differential Privacy} enables text-to-text privatization by adding calibrated noise to the vector of a word derived from an embedding space and projecting this noisy vector back to a discrete vocabulary using a nearest neighbor search. Since words are substituted without context, this mechanism is expected to fall short at finding substitutes for words with ambiguous meanings, such as \textit{'bank'}. To account for these ambiguous words, we leverage a sense embedding and incorporate a sense disambiguation step prior to noise injection. We encompass our modification to the privatization mechanism with an estimation of privacy and utility. For word sense disambiguation on the \textit{Words in Context} dataset, we demonstrate a substantial increase in classification accuracy by $6.05\%$

Guiding Text-to-Text Privatization by Syntax

Metric Differential Privacy is a generalization of differential privacy tailored to address the unique challenges of text-to-text privatization. By adding noise to the representation of words in the geometric space of embeddings, words are replaced with words located in the proximity of the noisy representation. Since embeddings are trained based on word co-occurrences, this mechanism ensures that substitutions stem from a common semantic context. Without considering the grammatical category of words, however, this mechanism cannot guarantee that substitutions play similar syntactic roles. We analyze the capability of text-to-text privatization to preserve the grammatical category of words after substitution and find that surrogate texts consist almost exclusively of nouns. Lacking the capability to produce surrogate texts that correlate with the structure of the sensitive texts, we encompass our analysis by transforming the privatization step into a candidate selection problem in which substitutions are directed to words with matching grammatical properties. We demonstrate a substantial improvement in the performance of downstream tasks by up to $4.66\%$ while retaining comparative privacy guarantees